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Thread: What makes QFT and GR incompatible?

  1. #1 What makes QFT and GR incompatible? 
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    I apologise if my question is a little stupid or obvious; but what makes Quantum field theory and general relativity incompatible.
    I would also perhaps like to know how string theory solves this issue.
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    Administrator Markus Hanke's Avatar
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    There are a great many reasons, most of them pretty technical, but the main issue would be that QFT is probabilistic in nature, whereas GR is inherently deterministic, and hence classical.

    String theory approaches this issue by postulating an object ( String ) which can potentially model the quantum mechanical behaviour of particles, while only being mathematically self-consistent in a space-time background goverened by the laws of GR. It thus incorporates both worlds. Bear in mind though that String theory is at present purely hypothetical.
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    Quote Originally Posted by Markus Hanke View Post
    There are a great many reasons, most of them pretty technical, but the main issue would be that QFT is probabilistic in nature, whereas GR is inherently deterministic, and hence classical.
    I don't understand. The same can be said of QFT and special relativity, can't it? Are they incompatible too?
    The most important thing to keep in mind is that you don't know everything and nobody else does either.
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    Quote Originally Posted by PhyMan View Post
    I don't understand. The same can be said of QFT and special relativity, can't it? Are they incompatible too?
    "Incompatible" is probably not a good term. QFT and GR are also not incompatible as such; it is possible to formulate a QFT in curved space-time, just as it is possible to describe a (special) relativistic electron, for example. The problems arise only once we try to formulate a quantized version of gravity.
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    Quote Originally Posted by Markus Hanke View Post
    "Incompatible" is probably not a good term. QFT and GR are also not incompatible as such; it is possible to formulate a QFT in curved space-time, just as it is possible to describe a (special) relativistic electron, for example. The problems arise only once we try to formulate a quantized version of gravity.
    I was doing some reading in this area and have come to learn that one of the main problems is that they're not sure how much space and time should go together. People often mistake relativity as doing away with the seperate concepts of space and time and have unified them into one concept, that of spacetime. But. as Einstein said, that's only true mathematically, not physically. As Richard C. Tolman wrote in his text, you can't rotate a clock into a rod.

    By the way, I recently came across the website of Edwin Taylor. It seems as though there will be a second much more expanded version of Exploring Black Holes coming out later this year. It's now online for the world to read. See Exploring Black Holes The MIT cosmologist Edmund Bertschinger is now one of the authorswheras before it was only Taylor and Wheeler. I took a look at parts of the book. It looks supurb! Especially the cosmology sections. Yay!
    The most important thing to keep in mind is that you don't know everything and nobody else does either.
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    Administrator Markus Hanke's Avatar
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    As Richard C. Tolman wrote in his text, you can't rotate a clock into a rod.
    Are you sure ? A clock is an extended object in time, just as a rod/ruler is an extended object in space. I see little difference between them.
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    mvb
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    Quote Originally Posted by Markus Hanke View Post
    "Incompatible" is probably not a good term. QFT and GR are also not incompatible as such; it is possible to formulate a QFT in curved space-time, just as it is possible to describe a (special) relativistic electron, for example. The problems arise only once we try to formulate a quantized version of gravity.
    GR is not my area of expertise, but I would imagine that there would be problems formulating GR in a world in which you only know the mass distribution probabilistically. Does anyone know whether this is true or not?
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by mvb View Post
    GR is not my area of expertise, but I would imagine that there would be problems formulating GR in a world in which you only know the mass distribution probabilistically. Does anyone know whether this is true or not?
    Definitely true. The stress-energy-momentum tensor, which acts as the source term of the gravitational field in GR, is not a probabilistic object. In fact it is the conserved Noether current associated with space-time translation invariance, hence I see no way how to make it "probabilistic".
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    KJW
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    Quote Originally Posted by Markus Hanke View Post
    Are you sure ? A clock is an extended object in time, just as a rod/ruler is an extended object in space. I see little difference between them.
    I think Richard C. Tolman was being glib. Nevertheless, I think what he meant was that the Lorentz group is not a simply-connected manifold. The future and past light-cones disconnect the time-like regions from the space-like region. You can't rotate a time-like interval to a space-like interval because the angles involved in Lorentz transformations of time-like objects are hyperbolic angles.
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